Sample Size for Parallel Analysis and Not-So-Common Criteria for Dimensions in Factor Analysis:Modifying the Eigenvalue > 1 Kaiser Rule

Abstract

This study investigated the performance (i.e., consistency and correctness) of parallel analysis (PA) compared to other criteria for selecting the number of dimensions (i.e., components or factors) to extract, which is a step prior to exploratory factor analysis (EFA). Common criteria included PA using original/unreduced correlation matrices with 1s on the diagonal (PACOR); PA using reduced correlation matrices with squared multiple correlations on the diagonal (PASMC); minimum average partial (MAP); and Kaiser’s eigenvalue-greater-than-one rule or average root (K1). Not-So-Common criteria included indicator function (IND), imbedded error (IE), modified average roots (MARs), and broken stick (BS). These same criteria were studied from existing real test data (Experiment I) and generated data (Experiment II) to expand the generalizability of the results to real-world data and to explore more conditions with more variables, respectively. Ultimately, we provide guidelines on employing these criteria to yield the best results under studied conditions.